How far could the Arabs gone in the conquest of Rome?
The Arabs had a small window to replicate their success in OTL. It would require the Romans and Persians to be exhausted in war. It also requires Romans/Persians to be led by incompetent commanders compared to the Arabs.
If this goes into a long protracted war, the arabs wont have the same resources as the Romans nor the Persians. Due to limited resources, they need to keep winning each battle until they conquer a good resources base.
Islam spread into South India and SE Asia by almost totally peaceful methods. It did pretty well for itself in SEA becoming the dominant religin of the Malay world and there's still a large Muslim population in S India.
This is under the assumption that they dominate the trade in the Red Sea and Indian Ocean.
Had the Arabs lost, the Red sea would be dominated by the Coptics- Egyptians, Romans or Ethiopians.
The Indian Ocean would be a toss up between the Coptics and the Persians.
I dont know with what resources the Arab would dominated the trade in ATL when they are limited in Arabia since by OTL trade in South East Asia, the Arabs had so much resources from Spain to Persia.